A fixed-point formula for Dirac operators on Lie groupoids
Abstract
We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group. We use the Getzler rescaling method to derive a fixed-point formula for the pairing of a trace with the K-theory class of such a family. For the pair groupoid of a closed manifold, our formula reduces to the standard fixed-point formula for the equivariant index of a Dirac operator. Further examples involve foliations and manifolds equipped with a normal crossing divisor.
Keywords
Cite
@article{arxiv.2307.11061,
title = {A fixed-point formula for Dirac operators on Lie groupoids},
author = {Ahmad Reza Haj Saeedi Sadegh and Shiqi Liu and Yiannis Loizides and Jesus Sanchez},
journal= {arXiv preprint arXiv:2307.11061},
year = {2024}
}
Comments
51 pages. Brief section on proper actions of non-compact groups added. Simplification of the fixed-point calculation. Further explanation added to sections on group actions and vanishing theorem. Author information updated